Question

A model airplane of mass 1.2 kg is attached to a horizontal string and flies in a horizontal circle of radius 6.5 m, making 1.6 revolutions every 8 s. (The weight of the plane is balanced by the upward "lift" force of the air on the wings of the plane.) The accelaration due to the gravity is 9.81 m/s² . Find the speed of the plane.

Answer 1

The speed of the model airplane is calculated using the formula for circular motion. With a radius of 6.5 m and completing 1.6 revolutions every 8 seconds, the speed is found to be approximately 8.17 m/s.

Step-by-step explanation:

The student has a question about finding the speed of the airplane which is flying in a horizontal circular motion. The formula for the speed (v) in circular motion is v = 2πr / T, where r is the radius (6.5 m) and T is the period, which is the time it takes to make one full revolution.

To calculate the speed, we first find the period of one revolution. As the airplane makes 1.6 revolutions every 8 seconds, we can calculate the period (T) for one revolution as follows:

T (for one revolution) = 8 s / 1.6 rev = 5 s/rev

Now, we calculate the speed:

v = 2πr / T = 2π * 6.5 m / 5 s = 8.17 m/s (approximately)

Therefore, the speed of the model airplane is about 8.17 m/s.